optex optimization expert system

OPTEX OPTIMIZATION EXPERT SYSTEM

A NEW APPROACH TO MAKE HIGH COMPLEXITY LARGE-SCALE MATHEMATICAL MODELS

THE FIRST STEP IN INDUSTRY 4.0 REVOLUTION : THE BEST WAY TO MAKE SOFTWARE IS HAVEN’T TO DO IT

Ing. Jesús Velásquez-Bermúdez, Dr. Eng. Chief Scientist DecisionWare - DO Analytics

[email protected]

mailto:[email protected]


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1. INTRODUCTION

OPTEX is the DO ANALYTICS (DOA) optimization technology.

The paper The Future of Mathematical Programming presents the future of OPTEX:

https://www.linkedin.com/pulse/future-mathematical-programming-jesus-velasquez/

1.1. ADVANCED ANALYTICS PROFESSIONALS

Consistent with the development of the Artificial Intelligence, Automation has come to stay, to the field of the

Advanced Analytics, where analysts and modelers received help of robots to do their job; Tomas Davenport, in his seminal book "Competing on Analytics", displayed three types of professionals involved with Analytics: i)

Amateur, ii) Semi-professional and iii) Professional, twelve years after the publication of the book, comes a new type of professional: the "robotizer", professionals that make algorithms which, in turn, make advanced

analytical algorithms, this speed-up the process of use of Advanced Analytics for those organizations that

believe in it, and therefore opening more gap with those who do not believe.

Analytical Robot:Professionals that create

Expert Computer Algorithms

that create

Advanced Analytics Algorithms

1.2. INDUSTRY 4.0 REVOLUTION

Industry 4.0 is a name given to the current trend of automation and data exchange in manufacturing

technologies. It includes cyber-physical systems, the Internet of things, cloud computing and cognitive computing. Industry 4.0 is commonly referred to as the fourth industrial revolution. Industry 4.0 fosters what has been

called a "smart factory". Within modular structured smart factories, cyber-physical systems monitor physical

processes, create a virtual copy of the physical world and make decentralized decisions. Over the Internet of Things, cyber-physical systems communicate and cooperate with each other and with humans in real-time both

internally and across organizational services offered and used by participants of the value chain. (Wikipedia).

OPTEX Optimization Expert System is a robot, based on concepts of Artificial Intelligence, that writes advanced analytics algorithms that are required for the digital transformation of enterprises, OPTEX automatically

linking them to the enterprise information system; in summary, OPTEX is a skilled robot that creates robots for

complex processes using advanced mathematical methodologies (state-of-the-art). This robotization process is at the highest level of automation, because it does not replace manual human work but supports the construction

https://www.linkedin.com/pulse/future-mathematical-programming-jesus-velasquez/


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of robots replacing human cognitive tasks, related to the modeling of stochastic processes or business/industrial processes optimization. OPTEX is result of praxis, since it has been used in several industrial/commercial projects

that give rise to practices included in OPTEX.

OPTEX increases productivity of mathematical modeler; understanding productivity such as: make more models

in less time, ensuring the quality of the produced algorithms. For this purpose, the process of mathematical modeling has been normalized and standardized, this makes OPTEX independent of industrial mathematical

technologies. As well as in the manual work robots enhance human ability, in the cognitive process, robots promote knowledge, systematized all tasks that are repetitive.

The cognitive robots are fundamentals for Industry 4.0.

1.3. A NEW APPROACH TO MAKE LARGE-SCALE MATHEMATICAL MODELS

OPTEX reduces to the minimum the cost of developing mathematical models; proposes a new way to implement optimization software, which traditionally involves the implementation of one "executable" program for each

model. Since its birth in 1991, OPTEX is conceived as a meta-tool (a robot, an expert system) that allows the

development of "all" mathematical models required in just one work environment. OPTEX “automatically” integrates information support system, generating a generic user interface that allow you to browse the tables of the information system. Last, but most important, OPTEX can generate models based on low-level programs

such as C, or high-level programs based on algebraic languages like GAMS, AIMMS, IBM ILOG OPL,... OPTEX ensures minimum implementation times, competitive computing times and portability of the mathematical models.

OPTEX make intensive use of large-scale methodologies, like Benders Decomposition.

Using OPTEX, the algebraic formulation of mathematical models is stored in a relational information system,

MMIS (Mathematical Models Information System), and therefore the tables that compose the MMIS can be loaded by any mechanism valid for manipulating tables, including EXCEL, while keeping the advantages of

relational databases. For this reason, DO ANALYTICS has developed OPTEX-EXCEL-MMS that enables

modelers, non-experts in optimization technologies or without knowledge of SQL (Structured Query Language), to solve complex mathematical problems associated with the database.

As part of the MMIS the modeler must develop the “data model”, tables that should fill the end-user. This system,

called IDIS (Industrial Data Information System), can reside on DBF tables, EXCEL books, CSV files or any SQL server data type (ORACLE, DB2, SQL Server, MySQL,...).

One of the advantages of separate the algebraic formulation from the optimization technology is that the modeler is not required to know the syntax of the optimization technology to implement the mathematical model, instead

focusing his efforts on the algebraic formulation and complete records of the tables in accordance with given instructions (filling forms/templates). The generated code is error-free, it is the result of many experiences that

ensure quality and proper operation; the modeler can learn from the code generated by OPTEX

After formulating the mathematical model, the user has two choices: i) to load the tables in the data base MMIS

or ii) to maintain EXCEL formulation and control the execution from the OPTEX-EXCEL-MMS interface or from the OPTEX web interface. In any case, OPTEX is responsible for generating the algorithm program for the

associated model.


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One of the biggest advantages of this approach is that it minimizes the time of development of mathematical

models that can be implemented quickly, by expert mathematical modelers that do not require deeper knowledge in: i) programming optimization languages, ii) large scale optimization methodologies, iii) SQL statements to

connect databases and iv) programing languages to make data displays; converting the time saved in avoided cost.

This makes of OPTEX a fast computing meta-platform oriented to the design, implementation, start-up and maintenance of DSSs based on a philosophy of concurrent development, in real time. Therefore, reducing the

development work of computer programs to a minimum (maybe “zero”). It translates into the immediate availability of additions and/or changes in the models, then the time can be used more effectively in the

mathematical modeling process and in the design of the interface DSSs with other tools of the user organization,

as may be the BI, ERP, WMS, …

OPTEX supports all activities required to implement "real-life" solutions, the process to follow for each mathematical model can be summarized in the following steps:

1. Mathematical modeling, whose product is a conceptual algebraic model; 2. Data Modeling, whose product is the data model of an information system;

3. Automatic implementation of the information system;

4. Generation of optimization programs that are capable of generate the numerical problems 5. Solving the problem using numerical algorithms specialized in accordance with the format of the problem;

6. Storage solution in the information system; and 7. Query and routing the results of the model.

The following diagram shows the process when working with base on EXCEL: i) algebraic model in the blackboard, ii) algebraic formulation in templates in MS-WORD, iii) algebraic formulation in tables in MS-EXCEL, iv) algebraic

formulation in csv format in ANSI standard, v) import the csv files to OPTEX-MMIS, vi) computer algorithm of the model in an optimization technology.


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ALGEBRAIC MODEL

FILLING TABLES

MODEL IN EXCEL

.CSVFILES

PARÁMETROS

Parámetro Descripción Uni

dad

Tabla

Referencia Campo

CTMItd Costo de inversión de referencia mínimo si se instala un biodigestor con tecnología td

$ MAE_TBD CTMI

CIFAtd,tr Costo de inversión asociado al tramo tr si se instala un biodigestor con tecnología td

$ TBD_TCI CIFA

FCTDud,td Factor de ajuste de costos de inversión para la tecnología td en el

sitio ud UDB_TBD FCTD

CIMIud,td

Costo de inversión de referencia mínimo si se instala un biodigestor con tecnología td en el sitio ud. Se calcula con base en la siguiente fórmula:

CIMIud,td = FCTDud,td × CTMItd

$

CTVBud,td,tr

Pendiente del tramo tr para el costo de inversión variable de un biodigestor con tecnología td en el sitio ud. Se calcula con base en

la siguiente fórmula: CIVBud,td,tr =

FCTDud,td × (CIFAtd,tr+1 – CIFAtd,tr) / (CALTtd,tr+1 – CALTtd,tr)

$/m3-día

CAMItd Capacidad de procesamiento mínima de un biodigestor con tecnología td.

m3-día MAE_TBD CAMI

CALT td,tr Capacidad de procesamiento asociada al tramo tr para un

biodigestor con tecnología td. m3-día TBD_TCI CALT

LOAD EXCEL

MODEL IN MS-WORD

LOAD OPTEX

MODEL IN A COMPUTER LANGUAGE

OPTIMIZATION TECHNOLOGY

OPL

CODE GENERATIONINCLUDING LARGE SCALE METHODOLOGIES

GAMS

DEVELOPING MATH MODELS - OPTEX FLOW CHART

1.4. OPTEX DECISION SUPPORT SYSTEMS

The following are Decision Support Systems developed using OPTEX:

OPCHAIN-HEALTH: Health Systems - Advanced Supply Chain Optimization

https://www.linkedin.com/pulse/opchain-health-dss-integrates-mathematical-models-during-velasquez/

OPCHAIN-E&G: Electricity & Natural Gas - Advanced Supply Chain Optimization

https://www.linkedin.com/pulse/electricity-natural-gas-advanced-supply-chain-jesus-velasquez/

OPCHAIN-SCO: Advanced Supply Chain Optimization. Traditional & State-of-The-Art Models

https://www.linkedin.com/pulse/supply-chain-optimization-jesus-velasquez/

OPCHAIN-DCO: Scientific Marketing: Advanced Demand Chain Optimization https://www.linkedin.com/pulse/scientific-marketing-advanced-demand-chain-jesus-velasquez/

OPCHAIN-RPO: Integrated Regional Planning Cities & Regions: Smart, Analytical, & Sustainable

https://www.linkedin.com/pulse/integrated-regional-planning-cities-regions-smart-jesus-velasquez/

OPCHAIN-MINES: Mathematical Programming Applied to Mining & Metallurgical Industries

https://www.linkedin.com/pulse/mathematical-programming-applied-mining-metallurgical-jesus-velasquez/

OPCHAIN-OIL: OIL Supply Chain Optimization

https://www.linkedin.com/pulse/oil-supply-chain-optimization-jesus-velasquez/

OPCHAIN-SME/PYME: An Advanced Analytics Decision Support System to Be Used on Demand in the Cloud

https://www.linkedin.com/pulse/advanced-analytics-decision-support-system-used-demand-velasquez/

OPCHAIN-TSO: Optimization of Complex Transport Systems

https://www.linkedin.com/pulse/optimization-logistics-operations-ports-jesus-velasquez/ https://www.linkedin.com/pulse/logistics-operations-optimization-ports-ships-systems-jesus-velasquez/

https://www.linkedin.com/pulse/regional-transport-systems-optimization-jesus-velasquez/ https://www.linkedin.com/pulse/transport-revenue-management-optimal-pricing-case-ltl-jesus-velasquez/

https://www.linkedin.com/pulse/opchain-health-dss-integrates-mathematical-models-during-velasquez/

https://www.linkedin.com/pulse/electricity-natural-gas-advanced-supply-chain-jesus-velasquez/

https://www.linkedin.com/pulse/supply-chain-optimization-jesus-velasquez/

https://www.linkedin.com/pulse/scientific-marketing-advanced-demand-chain-jesus-velasquez/

https://www.linkedin.com/pulse/integrated-regional-planning-cities-regions-smart-jesus-velasquez/

https://www.linkedin.com/pulse/mathematical-programming-applied-mining-metallurgical-jesus-velasquez/

https://www.linkedin.com/pulse/oil-supply-chain-optimization-jesus-velasquez/

https://www.linkedin.com/pulse/advanced-analytics-decision-support-system-used-demand-velasquez/

https://www.linkedin.com/pulse/optimization-logistics-operations-ports-jesus-velasquez/

https://www.linkedin.com/pulse/logistics-operations-optimization-ports-ships-systems-jesus-velasquez/

https://www.linkedin.com/pulse/regional-transport-systems-optimization-jesus-velasquez/

https://www.linkedin.com/pulse/transport-revenue-management-optimal-pricing-case-ltl-jesus-velasquez/


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OPCHAIN-ASO: Advanced Analytics Applied to Academic Systems https://www.linkedin.com/pulse/universitycollege-scheduling-time-tabling-using-jesus-velasquez/

OPCHAIN-BANK: Optimization Applied in Financial Enterprises

https://www.linkedin.com/pulse/financial-enterprises-modeling-advanced-analytics-jesus-velasquez/

All OPCHAIN models can be used in the form Optimization As A Service (OAAS) in the cloud.

2. STRUCTURED MATHEMATICAL MODELING

Sort the elements that are part of a mathematical model around the concepts of information systems involves the need to structure the process of mathematical modeling in a way to store all elements in the tables of the MMIS;

this implies organize the mathematical model from an "universal" point of view such as an information system; then, it is possible to affirm that the information system that supports mathematical modeling in OPTEX is the

first step towards standardization and normalization of the algebraic formulation of mathematical models, which is needed to socialize the Mathematical Programming based in the portability of the models between optimization

technologies.

2.1. MMIS - MATHEMATICAL MODELING INFORMATION SYSTEM

The MMIS manages the following elements (objects, entities):

▪ Tables ▪ Fields

▪ Indexes ▪ Sets

▪ Variables ▪ Parameters

▪ Restrictions

▪ Equations ▪ Objective Functions

▪ Problems ▪ Models

▪ Decision Support Systems

▪ Application

From the above objects, four haven’t a universal definition: ▪ Problem: set of constraints;

▪ Model: set of problems; ▪ DSS: set of models; and

▪ Application: set of DSSs.

MMIS standardizes the management of entities and relationships centered about its database algebraic language

that allows management of linear and non-linear equations.

The above objects are critical to addressing large-scale problems by coordinating multi-problem models; OPTEX

is based on the vision that sees the Mathematical Programming as a standard that can be understood by any expert modeler, this standardization is so solid that ensures that the binding of Mathematical Programming

problems is a new problem of Mathematical Programming. OPTEX capitalized this advantage as the union/partition of two problems correspond to union/partition of the restrictions of the two problems, which is

performed based on tables that store the parameterization of the problems and not based on the union of two

https://www.linkedin.com/pulse/universitycollege-scheduling-time-tabling-using-jesus-velasquez/

https://www.linkedin.com/pulse/financial-enterprises-modeling-advanced-analytics-jesus-velasquez/


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computer programs, which it is more difficult, may be impossible, to standardize. For example, an integrated model of the electricity-gas system is the union of the equations of the two individual systems (gas & electricity)

plus the coordination constraints.

ELECTRICITY&

GAS

ELECTRICITY

GAS

=+

The MMIS handles all aspects of the formulation, the solution and the use of mathematical models. Conceptually, OPTEX groups information according to the steps that must be faced in the process of developing an application:

▪ Formulation of mathematical definitions;

▪ Formulation and solution of problems and models; ▪ Optimization connectivity libraries;

▪ Using models

2.2. SOLVING OPTIMIZATION PROBLEMS

The formats of problems that can be solved with OPTEX dependent of optimization libraries that are available to

the end-user, making it possible to formulate linear or non-linear models (LP, MIP, QP, QPQC, MECP, NLP,...).

In addition to solving the basic optimization problems, OPTEX includes several advanced services, for real-world problems, aimed at facilitating the implementation of large problems. Among the services offered OPTEX

generates models that includes:

▪ Variables for feasibility analysis. ▪ Initial pre-set value for any variable.

▪ Equations for re-optimization including fixed variables. ▪ Convex hull generation.

▪ Generation of multi-criteria Pareto efficiency frontiers ▪ Parallel/Distribute optimization of multi-problem models.

▪ Disjunctive optimization

▪ Large-scale optimization methodologies

2.3. INTEGRATION OF MULTIPLE MODELS AND PROBLEMS


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Due to the complexity of real systems, DSSs are composed of multiple mathematical models which are integrated

through the data stream, thereby generating the information required by the decision maker to address all hierarchic levels: strategy, tactic, operation and real-time operations. The connection of data and models defines

the decision-making chain, which supports management productivity of organizations.

The different models must share information stored on a common database, coherent and standardized, to allow

data integration along the decision-making chain, in which some of the outputs of a model becomes the inputs of the models of subsequent stages, so this coordinated effort guarantees "optimization" of the entire system, it

is impossible to obtain with a single model. Researchers and producers of technology solutions share this point of

view.

The concept of objects allows an OPTEX problem being part of several models and a restriction to be part of various problems and so on. This approach facilitates the handling of large-scale optimization models; since under

the partition and decomposition scheme, a model consists of several coordinated problems whose solution is performed in accordance with an optimization methodology like Bender Theory or Lagrangean Coordination.

The next diagram shows the integration of models of an DSS for the electric sector.

State EstimationDual

Kalman Filter

Electricity & GasMixed Non-Linear

Economic Dispatch

Statistical ModelsARIMA-GARCH

Electricity & GasEnergy Trading

&Risk Management

Electricity & GasUnit

Commitment

Supply Chain Design

Synthetic Generation

Maintenance Optimization

Electricity & GasRegulatedEconomic Dispatch

CompetitiveDispatch

Renewable Energy Sources

Forecasting

Smart GridsRegulatedEconomic Dispatch

Operations &Financial

Optimization

DistributionNetwork

Reconfiguration

DistributionNetwork Design

DemandResponse

Optimization

DemandForecasting

Workforce Management

System

Smart GridsEnergy Trading

&Risk Management

Smart GridsUnit

Commitment

COMMON

DATA MODEL

INFORMATIONSYSTEM

ELECTRICITY & GASOPTIMIZATION

SMART GRIDS OPTIMIZATION

2.4. PROGRAM CODE GENERATION

OPTEX generates programs of mathematical models in high-level algebraic languages, like GAMS, IBM ILOG OPL, MOSEL, AIMMS, AMPL, …, and in languages of general purpose like C and PYTHON (in development),

making it in a generic meta-platform that works as interface for multiple Mathematical Programming technologies

that do not support services offered by OPTEX.

For example, with GAMS; OPTEX facilitates to the user the connectivity between mathematical models and information system, aspect that is not explicitly considered in GAMS; in this way the modeler can generate GAMS

programs including SQL connectivity with the information system of the end-user.


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The C ANSI program generation allows to

develop applications based on complex process of interconnection models, which

can be personalized according with specific characteristics of end-user, indispensable

requirement when it comes to operative

solutions for industrial processes and product and/or person distribution.

The diagram presents the C program

structure.

2.5. LARGE SCALE & STOCHASTIC OPTIMIZATION

The concept of multi-problem model facilitates the implementation of Large-Scale Optimization Methodologies

(LSOM) based on multi-level partition and decomposition, using Bender’s Theory and/or Lagrangean Relaxation. DOA algorithmic developments are concentrated in large-scale methodologies rather than the solution of basic

problems. Focusing its research effort in generating effective computational codes to resolve such problems by

making use of the advantages that today offer computers with multiple CPUs and computer grids. Thus, the no-expert modeler in this type of technology can access them in multiple computing technologies.

Considering that large scale technologies are the necessary complement to the basic optimization solvers (IBM

CPLEX, GUROBI, XPRESS, … ), since the union of the two powers allow to solve larger and more complex

mathematical problems, OPTEX incorporated as part of its services the automatic generation of computer algorithms using the variations and the improvements that have been developed by researchers.


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The screen allows the parameterization of a model using the Benders Theory so that the user can make a research to determine what methodology can be called the “best” for its specific problem. OPTEX includes various

variations of the basic theory like Generalized Benders Decomposition (GDP), Dual Benders Decomposition (DBD), Nested Benders Decomposition (NBD) and others.

For dynamic systems, OPTEX includes the GDDP (Generalized Dual Dynamic Programming) a large-scale

methodology developed by DOA for speed-up the solution time of large dynamic models compared with NBD which is based on the concept of L-Shape linear models. GDDP is applicable to any convex dynamic model (LP,

MIP, NLP, MINLP, NLP) and “some” non-convex models. The first version of GDDP was implemented in 1991; the first publication, in a Scientific Journal, in 2002.

OPTEX includes as part of their services the modeling of Multi-Stage Stochastic Programming (MS-SP) that

implies to handle random processes over the decision trees and solve problems with different types of objective

functions, for example: i) expected value; ii) MiniMax or Maximin and iii) maximum regret; additionally, OPTEX includes several alternative to risk management, including conditional-value-at-risk constraints (CVaR).

The conversion of deterministic (core) model to stochastic models is automatic, in the sense that the user must

only configure the conversion process and OPTEX generates the stochastic model from the deterministic

formulation. The problems are generated using "split" variables with non-anticipative constraints. The uncertainty dimensions may be defined by the users, considering which are the more convenient considering the type of

model and dynamic of the stochastics process. The solution of these problems can be accomplished through direct solution of equivalent deterministic problem or using large scale optimization methodologies. Sampling methods

may be included in the algorithms.

2.6. PARALLEL & DISTRIBUTED OPTIMIZATION

In the future, the real-life solution based on Mathematical Programing, applied to large physical and social

structures/organizations, must be based on multilevel parallelism using the modern computational architectures then, Large Scale Optimization Methodologies (LSOM) are the fundamental to atomize an

optimization/equilibrium mathematical problem in multiple types of sub-problems that can be solve using the

concepts of:

▪ Asynchronous Parallel Optimization (APO) (solving complex model using parallelization): defined as the solution of a large problem using the multiple cores of a workstation/server and/or a grid of computers;


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▪ Real-Time Distributed Optimization (RT-DO): defined as the solution of a problem in which multiple agents work coordinately to permanently keep the system on the optimality path; an example is the

optimization of the energy smart grids.

KNOWLEDGEDATABASE

SERVER

OPTIMIZATIONSERVICES PROVIDER

OPTIMIZATION OF DISTRIBUTE SYSTEMSREAL-TIME DISTRIBUTED OPTIMIZATION

To implement the previous processes, mainly RT-DO, the management of multiple solutions of atomized-

problems is necessary; this implies to introduce the concept of optimization expert systems oriented to:

▪ Knowledge Accumulation that exist in the multiple’s solutions of problems. An example is to use the

Benders cutting planes of a run (k) in the next runs (k+1, k+2, …). The management of databases of solutions (primal & dual) can be used to warm up the repetitive models and speed-up their solution. The next

diagram describes the situation.

OPTIMIZATION

INFORMATION

SYSTEM

Min t j h CTt(GTjth)

Subject to:

GDzth - uTN(z) LDuzth = 0

GDzth + GHAzth + DEFzth = DEMzth

ENuth - jL1(u) GTEjuth

- vL2(u) LLvuth = 0

OPTIMIZATIONK


Subject to:




- vL2(u) LLvuth = 0

OPTIMIZATIONK+1

CUTTING PLANES

KNOWLEDGEDATABASE

Sets & Parameters Read(K+1)

Primal & Dual Variables

Benders & Lagrangean Cutting Planes

Primal & Dual Variables

Benders & Lagrangean Cutting Planes


OPTIMIZATION KNOWLEDGE EXPERT SYSTEMCONNECTING MODELS DYNAMICALLY – CUTTING PLANES

▪ Knowledge Generation during the idle time of the computers pre-solving the complex part of a

large/complex mathematical models. This may be get representing the complex part as follow: i) using the convex-hull of optimal solutions, that may be solved when the computer is idle and ii) including the equations


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that represent the convex hull (normally a grid) in the integrated model. The next diagram describes the situation.

OPTIMIZATION

INFORMATIONSYSTEM

CONVEXHULL

KNOWLEDGEDATABASE


Sets & Parameters Read

(K)

OPTIMIZATIONK+1


Subject to:




- vL2(u) LLvuth = 0

CONVEX HULL EQUATIONS

OPTIMIZATIONK


Subject to:




- vL2(u) LLvuth = 0

CONVEX HULL EQUATIONS

Min j h CTt(GTjth)




- vL2(u) LLvuth = 0

OPTIMIZATION KNOWLEDGE EXPERT SYSTEMCONNECTING MODELS DYNAMICALLY – CONVEX HULLS

2.7. OPTEX ALGEBRAIC LANGUAGE

OPTEX has an algebraic programming language, like GAMS or AMPL. The compilation process works in double

pass: first analyzes the program syntax and second analyzes the logical content of the program; if everything is correct it is linked with OPTEX-EXE. Since from an OPTEX program is possible to fill the tables of MMIS. For

programs editions the modeler can use NOTEPAD++, a customized free software.

3. OPTEX PROCESSORS


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OPTEX works like an integral system that offers to the modeler a range of possibilities that guarantees efficiency and flexibility to face the implementation process of a decisions support system oriented to be launched in an

end-user. The modules that integrates OPTEX are presented below.

3.1. OPTEX-GUI: INTEGRATED DEVELOPMENT ENVIRONMENT

OPTEX-GUI corresponds to the IDE interface (Integrated Development Environment) used by the modeler and

its objective is to facilitate the access to all tables that integrated the DSS, this means MMIS or IDIS.

The algebraic formulation stored in databases allows the mathematical modelers to work simultaneously as users

of LANs and/or WANs; this is one of the most important characteristics of OPTEX, not possible in the optimization technologies based in computer programs. OPTEX-GUI is a client application that works in MS-WINDOWS

available for those who has installed OPTEX in their computers.

OPTEX-GUI is based on a browser like “windows explorer” that allows the user to access all tables of MMIS and

of IDIS; also, it has processes services which can be accessed through menus application. The connection to the tables is performed without programming tasks, in this way the modeler parametrize the way used by the end-

user to access to the IDIS tables.

OPTEX-GUI allows to the modeler interact with the MMIS in such a way that he can update the model equations

as the changes are required. OPTEX-GUI includes an online help system, providing to the modeler the necessary information about different aspects of the application that is being developed.

The next images show the explore window of final user and the shell window to see a master table and all related tables.


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3.2. OPTEX-EXE: INTERACTIVE SOLVER

OPTEX-EXE processor is responsible of perform all tasks related to the optimization services offered by OPTEX.

OPTEX-EXE has an interactive control interface allowing the modeler to conduct, step by step, the optimization processes; also, it can be executed as a task in the back-end for automatic processing, controlled by a

configuration file. This is only available for users with OPTEX installed on their computer. This interface can be activated from OPTEX-GUI and it works on MS-WINDOWS environments.

OPTEX-EXE is designed to act as client and as optimization server, in this way the implementation of a “cloud” environment solution using a remote server focuses on the implementation of OPTEX-EXE in both computers

with its corresponding parameterization.

The next table describes the steps to work with OPTEX-GUI and OPTEX-EXE

STEPS IN THE IMPLEMENTATION OF OPTEX APPLICATIONS

STEP DESCRIPTION

1

ALGEBRAIC MODEL LOAD The process begins with the load of the algebraic model by the responsible administrator/modeler of the model being implemented. This process implies to fill the corresponding database to the MMIS, this process must follow general guidelines describe bellow and it is performed through the access to OPTEX-GUI or to OPTEX-EXCEL-MMS.

2

MODEL DATA LOAD The process of defining the data model of IDIS is a process that is generated simultaneously with the loading of mathematical models so, as relations between the two models are strong so that the table structures are determined by the structure of the mathematical model, primarily by the relation between sets, parameters, variables and constraints. This process is performed through access to OPTEX-GUI or to OPTEX-EXCEL-MMS.


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STEPS IN THE IMPLEMENTATION OF OPTEX APPLICATIONS

STEP DESCRIPTION

3

GENERATION OF THE VISUAL USER INTERFACE OPTEX GUI provides services to generate a user interface without programming tasks, this involves organizing the shell windows in tables associated with a main table and the related secondary tables. This query is performed through the administrator who must built menus to provide access to end-users. This process is performed through access to OPTEX-GUI.

4 USING OPTEX-EXE Once the database is loaded into MMIS, the next step is to interact with OPTEX-EXE in order to begin the process of adjustment of the formulation of algebraic models.

5

ANALYSIS ALGEBRAIC MODEL The analysis of the algebraic model involves interaction coordinating two simultaneous activities : ▪ Review loaded algebraic formulation into MMIS; and ▪ Review the results obtained with the models.

5a REVIEW ALGEBRAIC MODEL FORMULATION This activity is carried out mainly with the RTF document generated by OPTEX, where the user can see the exact formulation loaded in MMIS, and find errors in it and/or the needs for adjustments due to imperfections in modeling.

5b STORAGE ALGEBRAIC MODEL RESULTS This activity is performed automatically by OPTEX-EXE and/or by the programs generated with OPTEX.

5c

REVIEWING THE RESULTS OF THE ALGEBRAIC MODEL This activity is mainly observing the results produced by the algebraic model that is being implemented as a result, the user can found errors in the data loaded in IDIS and/or the need for adjustments due to imperfections in modeling. This process is performed through access to OPTEX-GUI.

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SETTING THE ALGEBRAIC MODEL Following the analysis of the development and results in the early stages of implementation, it is necessary to make changes to the MMIS and IDIS. This cyclic process ended when the modeler considers that the implemented model produces the correct results and it is ready to be delivered to the end-user.

7 DATA ACCESS BY THE END-USER Finally, the end-user can access to use the model, which is made based on the data stored in the IDIS and results generated by the models.

DATA MODEL

INFORMATION SYSTEM

DATABASE ALGEBRAIC LANGUAGE

MODELS IN PROGRAMS

C - GAMS - OPL

RTF

DESIGNIMPLEMENTATION

MANUAL

END USERVISUAL

INTERFACE

MODELER

USERS

OPTEX-EXEPROCESSOR

OPTEX-GUI

1

2

3

4

5a

6

7

5c

END USER

5b

3.3. OPTEX-EXCEL-MMS: EXCEL OPTIMIZATION EXPERT SYSTEM

As already indicated, the data corresponding to the formulation of mathematical models is stored in the MMIS

and therefore the information system can be loaded for any valid mechanism for loading database, with EXCEL one of the most popular tools for processing tables.

The advantage of loading the mathematical models through tables is that the modeler does not require to know

programming languages to implement the mathematical models. After load the mathematical model in EXCEL,


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the tables can be loaded into the database OPTEX or kept in EXCEL; in any case OPTEX is responsible for generating the code associated to the programming language that the modeler has selected.

OPTEX-EXCEL-MMS controls the processes to be performed with OPTEX from EXCEL when the user has

installed OPTEX on his computer or when the user access to OPTEX optimization server. The process was described previously. The following figure shows the results in the OPTEX-EXCEL-GUI, part OPTEX-EXCEL-

MMS.

3.4. OPTEX-WEB: OPTEX WEB ACCESS SERVICE

OPTEX-WEB: Modeler interface oriented to using EXCEL as a way to develop models. Available on a website

controlled by DO ANALYTICS or by an OPTEX user.


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4. IDIS: INDUSTRIAL DATA INFORMATION SYSTEM

The data that represents the technical and socio-economic information of the industrial system are stored in the IDIS, classified into two types:

▪ IIS: Permanent Industrial Information System, corresponding to the tables of the information system that are independent of any scenario (case study); and

▪ SIS: Scenarios Information System, corresponding to the tables that represents the variability of scenario.

The IDIS data model depends on mathematical

models; the content stored in tables depends on the physical system modelled and on the scenarios that

the user wants to analyze. OPTEX-GUI provides services to configure the IDIS data model and its

user interface; both IIS and SIS are relational

information systems whose data models depend on mathematical models.

The scenarios are grouped under the concept of

scenario families, so that the user can perform cross analysis of all scenarios that belong to a family. SIS

corresponds to the union of information systems of

each scenario.

SCENARIOS INFORMATION SYSTEM

Root DirectoryScenarios

Information System

Directory

Family1

DirectoryFamily

E

DirectoryFamily

F

DirectoryScenarioNo. E-E

DirectoryScenarioNo. E-1

TablesParameters

Sets

TablesParameters

Sets

TablesVariables

Constraints

TablesParameters

Sets

TablesVariables

Constraints

DirectoryScenarioNo. E-X

TablesParameters

Sets

TablesVariables

Constraints

OPTEX provides services for the development and implementation of the data model and corresponding user interface; thus the development of mathematical models of the corresponding system information and the visual

interface is limited to a process of filling tables.


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4.1. SQL CONNECTIVITY SERVICES

To support the IDIS information system, OPTEX provides connectivity services with tables stored in EXCEL,

CSV, DBF and SQL server type, connected via ODBCs (Open DataBase Connectivity). The following picture shows the SQL connection for loading data into a IBM ILOG OPL program

OPTEX provides the following services to support IDIS:

▪ Structuring the data model ▪ Generation user interface for access to IDIS tables.

▪ Check the integrity of the database

▪ Generation of derived tables for integration between OPTEX models and other computer systems. ▪ Generation of SQL statements for connection with optimization technologies

▪ Automatic mapping with other information systems (ERP, WMS, TMS, GIS, ...) ▪ Import/Export Data

▪ Structured query of IDIS tables.

4.2. RESULTS STORE & DISPLAY

In OPTEX -GUI the modeler has access to tables that contains the results of variables and constraints for each

specific scenario.

A fundamental part in the implementation of a decision support system is its ability to display the results associated

to mathematical models that produce millions of data (big data). OPTEX approach facilitates the linking of results with information technology tools aimed at the exploration and visualization of large data volumes. All results of

mathematical models, primary and dual variables, independent of optimization platform. Data is stored in relational tables that can be consulted by the user through OPTEX-GUI.


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Based on this approach OPTEX can generate XML interfaces with EXCEL, MS-Project, IBM-Jviews,

TABLEAU, QLIKVIEW and Mondrian OLAP Server. The following image shows an example of displaying a

routing program in IBM-Jviews.


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5. DOCUMENTATION

OPTEX generates RTF documents (Rich Text Format), visible and editable with text editors’ programs like MS-WORD. The RTF contains all the mathematical formulation included in a mathematical model. Thus, it guarantees

proper documentation of the implemented models. Following, an example of the generated documentation.

RESTRICTIONS – MODULO:

RESTRICTION DESCRIPTION – EQUATION DISJUNCTIVE

VARIABLE

BIEVt,j,hh

DECx1000

Existencias Máximas de Producto Final más Envase en Centros de Distribución

pPT(j) vPVJ(p j) ICEt,j,p,v,hh + vJV(j) EVJt,j,v,hh ACEj

t jPUN hh_DIM_hh(*)

Índices: t Período

j Centro Distribución hh Escenario Demanda p Producto

v Envase

Conjuntos: pPT(j) Productos Cerveceros x Centro de Distribución j

vPVJ(p,j) Envases x Producto x Centro de Distribución j

vJV(j) Envases x Centro de Distribución j

jPUN Centros de Distribución (j)

hh_DIM_hh(*) Dimension hh <- Escenario Aleatorio

Parámetros:

ACEj Capacidad Almancenamiento del Centro de Distribución (UNDx100) Variables:

ICEt,j,p,v,hh Existencias de Producto Finalizado en Centros de Distribución (DECx10) EVJt,j,v,hh Existencias Envase Vacío en Centros de Distribución (DECx10)

…

… …

WHEt,l,hh

Hrs

Tiempo Trabajado en Línea de Empacado. NO incluye tiempo preparación Línea

HOEt,l,hh + HEEt,l,hh - pLP(l) vLTV(l p) KWEl,v × PCEt,l,p,v,hh = 0

t lLN hh_DIM_hh(*)

Índices: t Período

l Línea Envasadora hh Escenario Demanda

p Producto v Envase Conjuntos:

pLP(l) Productos x Línea de Envase

vLTV(l,p) Envases x Línea de Envase x Producto

lLN Línea de Envase

hh_DIM_hh(*) Dimensión hh <- Escenario Aleatorio

Parámetros: KWEl,v Velocidad de Producción de Línea Envasadora (Hrs/UNDx100)

Variables: HOEt,l,hh Horas Ordinarias de Producción en Líneas de Envasado (Hrs) HEEt,l,hh Horas Extras de Producción en Líneas de Envasado (Hrs)

PCEt,l,p,v,hh Volumen de Envasado de Cerveza en Líneas Envasadoras (DECx10)

Reports include the description of the data model and the link between the fields of each table and the sets and

the parameters of the models that are read as input data.


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6. OPTEX OPTIMIZATION SERVER

Following the actual trend of cloud solutions, OPTEX allows the development of applications oriented to solve optimization problems, using services provided on the Internet (cloud services). For client-server applications

OPTEX considers four roles that interact between them, allowing multiple architectures configured according to

user needs: ▪ OPTEX-GUI: Graphical interface that allows to the administrator and users to view OPTEX information

system. ▪ OPTEX-CLIENT: Processor oriented to provide OPTEX services on a client computer that uses a model

locally or establishing a connection to a remote server that provides services to solve optimization problems.

This role can be assumed by OPTEX-EXE, OPTEX-EXCEL-MMS and OPTEX-WEB. The final user can build his own OPTEX-CLIENT.

▪ OPTEX-CONTROL-SERVER: Task dedicated to manage the connections from a remote server with multiple clients requesting OPTEX services optimization.

▪ OPTEX-SERVER: Remote processor aimed at solving mathematical problems associated with an optimization model that has established a connection to apply the solution to a problem. OPTEX-EXE assumes this role.

Transferring files can be performed under any of the following ways: EXCEL books; CSV files or data stored on a SQL server to which access OPTEX-SERVER.

EXCEL - CSV

OUTPUT DATA

OPTEX CLIENT – SERVER ARCHITECTURE

EXCEL - CSV

INPUT DATA

SQL

INPUT DATA

SQL

OUPUT DATA

OPTIMIZATION SERVER

7. OPTEX DOWNLOADING

You can download a BETA version of OPTEX following the instructions included in the following presentation:

https://goo.gl/Y9zMHD. If you need more information or are interested in OPTEX please contact us via

[email protected]

https://goo.gl/Y9zMHD




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optex optimization expert system

Documents